相关论文: GIB: Imperfect Information in a Computationally Ch…

We investigate the complexity of finding a winning strategy for the mis\`ere version of three games played on graphs : two variants of the game $\text{NimG}$, introduced by Stockmann in 2004 and the game $\text{Vertex Geography}$ on both…

The break minimization problem is a fundamental problem in sports scheduling. Recently, its quadratic unconstrained binary optimization (QUBO) formulation has been proposed, which has gained much interest with the rapidly growing field of…

Limited lookahead has been studied for decades in perfect-information games. We initiate a new direction via two simultaneous deviation points: generalization to imperfect-information games and a game-theoretic approach. We study how one…

We review recent attempts at dealing with the sign problem in Monte Carlo calculations by deforming the region of integration in the path integral from real to complex fields. We discuss the theoretical foundations, the algorithmic issues…

The information bottleneck (IB) method offers an attractive framework for understanding representation learning, however its applications are often limited by its computational intractability. Analytical characterization of the IB method is…

Mixed-integer programming (MIP) technology offers a generic way of formulating and solving combinatorial optimization problems. While generally reliable, state-of-the-art MIP solvers base many crucial decisions on hand-crafted heuristics,…

The Monte Carlo evaluation of path integrals is one of a few general purpose methods to approach strongly coupled systems. It is used in all branches of Physics, from QCD/nuclear physics to the correlated electron systems. However, many…

In online betting, the bookmaker can update the payoffs it offers on a particular event many times before the event takes place, and the updated payoffs may depend on the bets accumulated thus far. We study the problem of bookmaking with…

This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous…

In this paper, we introduce three different classes of undergraduate research projects that implement model building and integer programming. These research projects focus on determining and analyzing solutions to the game The Genius…

This paper sets up a methodology for approximately solving optimal investment problems using duality methods combined with Monte Carlo simulations. In particular, we show how to tackle high dimensional problems in incomplete markets, where…

The maximum clique problem (MCP) is a fundamental problem in graph theory and in computational complexity. Given a graph G, the problem is that of finding the largest clique (complete subgraph) in G. The MCP has many important applications…

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of…

I show how to construct Monte Carlo algorithms (programs), prove that they are correct and document them. Complicated algorithms are build using a handful of elementary methods. This construction process is transparently illustrated using…

We investigate pruning in search trees of so-called quantified integer linear programs (QIPs). QIPs consist of a set of linear inequalities and a minimax objective function, where some variables are existentially and others are universally…

Cooperative Bayesian games (BGs) can model decision-making problems for teams of agents under imperfect information, but require space and computation time that is exponential in the number of agents. While agent independence has been used…

Automated design of multi-agent interactions with desirable equilibrium outcomes is inherently difficult due to the computational hardness, non-uniqueness, and instability of the resulting equilibria. In this work, we propose the use of…

Monte Carlo simulations away from half-filling suffer from a sign problem that can be reduced by deforming the contour of integration. Such a transformation, which induces a Jacobian determinant in the Boltzmann weight, can be implemented…

The maximum graph bisection problem is a well known graph partition problem. The problem has been proven to be NP-hard. In the maximum graph bisection problem it is required that the set of vertices is divided into two partition with equal…

Recently, Huggins et. al. [Nature, 603, 416-420 (2022)] devised a general projective Quantum Monte Carlo method suitable for implementation on quantum computers. This hybrid approach, however, relies on a subroutine -the computation of the…